The assumption that the servers never compare notes. Each one alone learns nothing. Together they could.
Why it matters: Common in privacy systems run jointly by independent organizations.
On the map: the servers never pool what they saw
The assumption that the servers in a protocol never pool what they saw. Each server alone learns nothing. Together they could reconstruct your query or data.
It is common in practice as "split trust" between independent organizations, for example Prio-style private aggregation[1], which was used for COVID exposure-notification analytics[2].
If any of these breaks, this breaks too.
If this breaks, these break with it.